Question

The domain and range of the function f given by f(x) = 2 – |x – 5| is ______.

Options

• Domain = R⁺, Range = `(– oo, 1]`

• Domain = R, Range = `(– oo, 2]`

• Domain = R, Range = `(– oo, 2)`

• Domain = R+, Range = `(– oo, 2]`

Answer 1

The domain and range of the function f given by f(x) = 2 – |x – 5| is Domain = R, Range = `(– oo, 2]`.

Explanation:

Given that: f(x) = 2 – |x – 5| 

Here, f(x) is defined for x ∈ R

∴ Domain of f(x) = R

Now, x – 5 ≥ 0

⇒ – |x – 5| ≤ 0

⇒ 2 – |x – 5| ≤ 2

⇒ f(x) ≤ 2

∴ Range of f(x) = `(-oo, 2]`